Generalized numerical differentiation in the turbidity spectrum method

The validity of the choice of the geometric mean wavelength in the differential version of the turbidity spectrum method is analyzed by numerical simulation. It is found that this choice can introduce errors, as large as 5–35%, in the estimated values of parameters of a colloid system. It is proposed to construct the calibrations n=n(α, m) by using the realistic (instrument-dependent) differentiation method, generalized in a way that provides for the monotonic nature of the calibrations.     

Cosmic ray electron spectrum due to the dispersion of injection spectrum

The cosmic-ray total electron spectrum(electrons plus positrons) has been measured precisely up to Te V energies,with more interesting features found.Exhaustive analyses of the electron spectrum strongly support a spectral hardening above 100 GeV,rather than a featureless single power-law,which is confirmed by the most recent observations.Meanwhile,the measurements of the DAMPE satellite have verified the presence of a knee-like structure around 1 TeV in the electron spectrum,resembling the cosmic-ray knee.In this paper,we establish a physical model in which the observed electron spectrum is composed of a superposition of CR sources with various spectral indices and high-energy cutoffs.The dispersion of the power index is assumed to be Gaussian,while the cutoff energy Ec follows a power-law distribution.These simple ideas can account naturally for both the hundred-GeV excess and the TeV spectral break.     

Observation of a dispersion transition and the stability of a liquid in a nanoporous medium

It has been found that the removal of overpressure is accompanied by a transition of some nonwetting-liquid nanoclusters to the stable state in narrow ranges of the filling factor and temperature. This means that the nonwetting liquid becomes ??wetting.??     

Refined calibrations of the turbidity spectrum for ill-defined disperse systems

A corridor type of calibration curves of the turbidity-spectrum method is proposed for ill-defined disperse systems. It is found that the cubic-mean radius of particles strongly depends on factors to which optical instruments have a low sensitivity. The concept of an effective cubic-mean radius is introduced and an algorithm for constructing corridor calibration curves for this radius is given on the basis of the method of realistic (instrument-dependent) differentiation, which was proposed earlier. An example of a calibration curve for a relative refractive index of 1.12 is presented.     

Allowance for instrumental factors in the turbidity and light-scattering spectrum methods

We calculated calibration curves for the turbidity and light-scattering spectrum methods by taking into account the nonmonochromaticity of filters in photoelectrocolorimeters (using the FEK-56 as an example) and nephelometers (using the NFM as an example). The allowance for the nonmonochromaticity was found to have virtually no effect on the calibrations in the former case and to shift them in the latter case. An example of a calibration curve is given for a relative refractive index of 1.12. We touch on the influence of the turbidity of a disperse system on the results of nephelometry.     

Evaluations of particulate mass loading from visibility observations and atmospheric turbidity measurements

Summary Three extinction models for urban aerosol particles, having Junge-type size distribution curves, were determined by using a very accurate computer programme based on Mie extinction theory for spherical particles. For each model, the volume extinction coefficients were calculated at seven visible and near-infra-red wave-lengths, for twenty-seven values of Junge parameter ranging from 1.8 to 4.4, and for five values of relative humidity from 0% to 85%. Moreover, the volume extinction coefficients produced by five monomodal models, based on log-normal size distribution curves for urban particles (composed of water-soluble substances, dustlike aerosol, and carbonaceous substances), were calculated at the seven wave-lengths and for five values of relative humidity from 0% to 90%. These monomodal models can be used to define bimodal and trimodal extinction models consisting of variable number fractions of small and large particles. Evaluations of the vertical particulate mass loading from sun photometer measurements and of particulate mass loading at ground level from visibility observations can be obtained by following the procedures suggested herein for both Junge-type and multimodal extinction models. Atmospheric turbidity and visibility measurements taken at various urban stations in the Po Valley were examined by means of the above procedures. The results show that in the cases in which ?ngstr?m's spectral exponent is relatively high (>1.3), Junge-type models give, reliable evaluations of the atmospheric particulate mass loading. In the other cases, the Junge-type extinction model and the bimodal models including the large urban particle mode can be used to determine the lower and the upper limits of particulate mass loading.

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Riassunto Tre modelli di estinzione per particelle atmosferiche di origine urbana, aventi curve di distribuzione dimensionale del tipo di Junge, sono stati definiti usando un programma di calcolo molto accurato per l'estinzione di Mie da parte di particelle sferiche. I coefficienti di estinzione di ogni modello sono stati determinati a sette lunghezze d'onda nel visibile e vicino infrarosso, per ventisette valori del parametro di Junge da 1.8 a 4.4 e per cinque valori dell'umidità relativa dallo 0% all'85%. Inoltre, i coefficienti di estinzione prodotti da cinque modelli monomodali, basati su curve log-normali della distribuzione dimensionale per particelle di tipo urbano (composte di sostanze solubili in acqua, polveri e sostanze carboniose), sono stati calcolati alle sette lunghezze d'onda e per cinque valori dell'umidità relativa dallo 0% al 90%. Questi modelli monomodali possono essere usati per definire modelli di estinzione bimodali e trimodali, composti da particelle di piccole e grandi dimensioni, in percentuali numeriche variabili. Seguendo i procedimenti da noi proposti sia per i modelli del tipo di Junge che per quelli multimodali, valutazioni realistiche del contenuto verticale della massa di particelle possono essere ricavate da misure di fotometria solare, mentre si possono ottenere buone stime del contenuto di massa per volume unitario al livello del suolo da osservazioni di visibilità. Diverse misure di torbidità atmosferica e visibilità eseguite in differenti località urbane della pianura padana sono state esaminate usando questi procedimenti. I risultati mostrano che nei casi in cui l'esponente spettrale di ?ngstr?m è relativamente alto (>1.3), i modelli del tipo di Junge forniscono stime affidabili del contenuto atmosferico di massa delle particelle. Negli altri casi, i modelli di estinzione del tipo di Junge e i modelli bimodali che contengono il modello monomodale di grandi particelle urbane possono essere usati per effettuare una stima di minima ed una di massima del contenuto atmosferico di massa delle particelle.

     

Evaluations of particulate mass loading from visibility observations and atmospheric turbidity measurements

Summary Two extinction models for continental and rural particles were defined by using a very accurate computer programme based on Mie extinction theory for spherical particles. The first extinction model gives several sets of volume extinction coefficients at seven visible and near-infra-red wave-lengths, calculated for twenty-seven Junge-type size distribution curves (with Junge parameter ranging from 1.8 to 4.4) and for eight relative-humidity values of the air. This model also gives the corresponding values of ?ngstr?m's exponent α and mean particle mass. The second extinction model gives similar sets of data, calculated for two lognormal size distribution curves of tropospheric and large rural particles at five relative-humidity values of the air. These monomodal models can be used to determine bimodal extinction models consisting of variable number fractions of tropospheric and rural particles. Evaluations of the particulate mass loading can be obtained from measurements of visual range and atmospheric turbidity, choosing the most appropriate extinction model on the basis of the spectral features characterizing atmospheric attenuation. Measurements of visibility and atmospheric turbidity in two rural localities of the Po Valley were examined by employing both the present extinction models and other extinction models commonly used. The comparison of the results shows that the Junge-type extinction model can be reliably used in cases in which the exponent α is equal to or larger than 1.4. For smaller values of α, the Junge-type extinction model and bimodal model were found to give realistic evaluations of the lower and upper limits of particulate mass loading.

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Riassunto Usando un programma di calcolo assai accurato, basato sulla teoria di Mie per l'estizione da particelle sferiche, si sono definiti due modelli di estinzione per particelle di origine continentale e rurale. Il primo di questi modelli fornisce diverse serie spettrali dei coefficienti di estinzione da particelle su percorso unitario, relativi a sette lunghezze d'onda nel visibile e vicino infrarosso e calcolati per ventisette distribuzioni dimensionali del tipo di Junge (con parametro di Junge che varia da 1.8 a 4.4) e per otto valori dell'umidità relativa dell'aria. Inoltre, questo modello fornisce i valori corrispondenti dell'esponente di ?ngstr?m α e della massa media delle particelle. Il secondo modello fornisce insiemi simili di dati calcolati per due distribuzioni dimensionali di tipo lognormale, relative a particelle troposferiche e a grandi particelle di origine rurale, e per cinque valori di umidità relativa dell'aria. Questi modelli monomodali possono essere usati per definire modelli bimodali di estinzione, composti da particelle troposferiche e rurali in percentuali numeriche variabili. Scegliendo il modello piú appropriato di estinzione sulla base delle caratteristiche spettrali di attenuazione atmosferica, si possono ricavare valutazioni del contenuto atmosferico di massa delle particelle da misure di visibilità e torbidità atmosferica. Misure di questo tipo, effettuate in due località rurali della pianura padana, sono state esaminate sia mediante i modelli di estinzione qui proposti sia mediante altri modelli di estinzione usati comunemente. Il confronto tra i risultati mostra che il modello di estinzione del tipo di Junge può dare risultati realistici nei casi in cui l'esponente α è maggiore di o egule a 1.4. Per valori minori di α, il modello di Junge e il modello bimodale forniscono rispettivamente una stima di minima e una stima di massima del contenuto atmosferico di massa delle particelle.

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Резюме Предлагаются две модели экстинции для континентальных и селяских частиц, используя очень точную программу, основанную на теории Ми сферических частиц. Первая модель экстинции дает несколько систем для коэффициентов общемной экстинции при семи длинах волн в видимом и ближнем инфракрасном диапазонах, которые вычислены для 27 распределений по размерам типа Джунджа (с параметром Джунджа в области от 1.8 до 4.4) и для восьми значений относительной влажности воздуха. Эта модель также дает соответствуюшие величины для экспоненты Ангстрема α и среднюю массу частиц. Вторая модель экстинции дает аналогичные системы данных, вычисленных для двух log-нормальных распределений по размерам для тропосферных и больших сельских частиц при пяти значениях относительной влажности воздуха. Эти мономодальные модели могут быть использованы для определения бимодальных моделей экстинции, которые учитывают изменяющиеся численные относительные содержания тропосферных и сельских частиц. Выбирая наиболее соответствуюшую модель экстинции на основе спектральных особенностей, характеризующих атмосфернэе ослабление, можно оденить массовое содержание микрочастиц из измерениц видимости и помутнения атмосферы. Анализируются измерения видимости и помутнения атмосферы в двух сельских райохах долины По, используя предложенные модели экстинции и обычно пременяемые модели экстинции. Сравнение результатов показывает, что модель экстинции типа Джунджа может быть надежно использована в случаях, когда экспонента α равна или больше, чем 1.4. Для меньших значений α получается, что модель экстинции типа Джунджа и бимодальная модель дают реалистические оценки для нижнего и верхнего пределов массового содержания микрочастиц.

     

关于介质吸收与色散的振子特性参数

根据共振模型，讨论影响介质的吸收与色散的振子特性参数，得到关于振子阻尼系数的振子数的解析式。据此，利用介质的吸收谱曲线可以定量计算振子的阻尼系数和振子数，这对研究和改善介质的吸收和色散特性有重要意义。我们已用此方法研究气液浓度的光电特性。     

The effect of spatial dispersion and boundaries of a medium on resonance radiation transfer

An integral equation is derived for the spectral density of excited atoms using optically dense bounded dispersion media as an example. It is found that the inclusion of the thermal motion of atoms and of the effects due to the existence of a boundary brings about a nonlocal correlation between the concentration of excited particles and the intensity of electromagnetic field in the medium. It is demonstrated that, when the spatial dispersion of permittivity and the boundary effects are disregarded, the obtained result transforms to the well-known Biberman-Holstein equation. The problem on the spectral intensity of radiation of a heated half-space is also investigated.     

双负介质对光子晶体透射能带谱的简并效应研究

利用传输矩阵法理论,通过数值计算模拟的方法,研究双负介质对一维光子晶体透射能带谱的影响。结果表明:当C介质由双正介质变成双负介质时,光子晶体(CBAABC)n的禁带、能带和光子晶体(AB)m(CBAABC)n(BA)m的透射峰均出现明显的简并现象,即前者相邻多禁带和多能带结构简并为较宽的单禁带和单能带结构,后者的透射峰由2n+1条简并成2n-1条;当双负介质C的光学厚度负值减小时,光子晶体(AB)m(CBAABC)n(BA)m的透射峰向禁带中心靠拢,出现简并趋势。双负介质对光子晶体透射能带谱的简并效应,为光子晶体设计光学滤波器件、光学开关等提供参考。     

介质对高频电磁波的色散关系

根据经典力学、电磁学知识和经典色散理论导出了介质对高频电磁波的色散规律,由此色散规律可以清楚看出几乎所有介质对于高频电磁波来说都成为透明介质,并以金属铜为例进行了验证.据此人们可以容易地理解高频电磁波的某些应用.     

Modulation response of dispersion cumulative medium to nonstationary quantum flux

Dynamics of cumulative medium with energy dispersion properties under the influence of quanta flux from nonstationary source is investigated. The intended purpose was to estimate the opportunity for the releasing phase in the spatial-temporal profile of the energy being accumulated by the medium. The examination showed that this opportunity does exist at the interaction of the fluxes characterized by rapid temporal variations of intensity with the weak-dispersion mediums. The latter provides favorable conditions for the modulation regime regarding to the dissipating energy.     

An iterative effective medium approximation (IEMA) for wave dispersion and attenuation predictions in particulate composites, suspensions and emulsions

In the present work we deal with the scattering dispersion and attenuation of elastic waves in different types of nonhomogeneous media. The iterative effective medium approximation based on a single scattering consideration, for the estimation of wave dispersion and attenuation, proposed in Tsinopoulos et al., [Adv. Compos. Lett. 9, 193-200 (2000)] is examined herein not only for solid components but for liquid suspensions as well. The iterations are conducted by means of the classical relation of Waterman and Truell, while the self-consistent condition proposed by Kim et al. [J. Acoust. Soc. Am. 97, 1380-1388 (1995)] is used for the convergence of the iterative procedure. The single scattering problem is solved using the Ying and Truell formulation, which with a minor modification can accommodate the solution of scattering on inclusions in liquid. Theoretical results for several different systems of particulates and suspensions are presented being in excellent agreement with experimental data taken from the literature.     

广义Helmholtz方程的Green函数及旋波介质色散关系的另一求解方法

运用并矢法求解广义Helmholtz方程,结合Fourier变换、留数定理等数学处理,给出方程的并矢Green函数解析表达式;并进一步就旋波介质给出其中色散关系的另外一种求解方法．     

汞光谱色散曲线实验研究

在现有理论基础上,利用汞光谱色散实验测出汞光谱8条谱线对棱镜的折射率后,通过多项式拟合得到了波长和折射率的经验关系,即色散特性函数,并由此得到了汞光谱的角色散率.本文有助于人们更深入认识色散现象.     

Born-fock approximation and dispersion properties of a resonant medium

A procedure of correct calculation of the dispersion series for polarization of a resonant nonlinear medium is proposed. For the example of an inverted two-level system the maximal time of the group advance is analyzed for a pulse propagating with the velocity exceeding the speed of light.